Question 11.5: Suppose there is an insurance pool that reimburses hospital ......
Suppose there is an insurance pool that reimburses hospital charges for 200 policyholders. Determine the expected claims payments, standard deviation and coefficient of variation where the claims for each individual are independent of others.
Let X_{i} represent the charges for policyholder X_{i}. The expected value of the hospital charges for the pool is given by
Let S=\textstyle\Sigma_{1}^{200}X_{i}. Then
E\left[S\right]=200\ *E\left[X\right]=200\ *1.5=300\sigma_{S}^{2}=200\ *\sigma_{X}^{2}=200*27.75=5500
\sigma_{S}=\;\sqrt{5500}=74.50(=\sqrt{200}*\sigma_{X})
The coefficient of variation is given by σ_{S}/E[S] = 74.50/300 = 0.25.
The insurance company will generally include a deductible (policy excess) that specifies the losses that will be reimbursed are only those that are in excess of a certain threshold value (stated by the excess value on the policy). This affects the expected claims payment and standard deviation for the insurance pool.